Possible Clues:

• Valueless river?
• Removed head of pointless flower
• Roofless dwelling by river
• River insect getting clear of lake
• Who has been dropping aitches in Yorkshire?
• River put to some purpose by duck
• River to The Wash
• Plunged naked into river
• I'd say trickle is current
• York, say, has no hotel, but it does feature this